2013 年度
第 4 回 九州大学 組合せ数学セミナー
Hakata Workshop 20141

下記のようにセミナーを開催しますので, ご案内申し上げます。
世話人:アドバイザー :溝口 佳寛（九大 IMI） 脇 隼人 (九大 IMI)
渋田 敬史（九大 IMI） 谷口 哲至（松江高専）
島袋 修（長崎大）
田上 真（九州工大）
栗原大武（北九州高専） 千葉周也 (熊本大)坂内 英一（上海交通大学/九大数理）記
日時: 2014 年 2 月 8 日 (土) 9:15–17:30
場所:Seminar Room R (4F) in Reference Eki Higashi Building (1-16-14 Hakata-EkiHigashi, Hakata-Ku, Fukuoka City, 812-0013)
URL: http://comb.math.kyushu-u.ac.jp/

プログラム

9:15–9:20 Opening （Tetsuji Taniguchi）
9:20–10:00 Shoichi Tsuchiya (Tokyo University of Science)
On Halin graphs and generalized Halin graphs
10:10–10:50 Shuya Chiba (Kumamoto University)
On the number of components of 2-factors in claw-free graphs
11:00–11:40 Masashi Shinohara (Shiga University)
On complementary Ramsey numbers
13:10–14:40 Poster Session
Software in Mathematics Demonstration Track
15:00–15:40 Michio Seto (Shimane University)
Graph homomorphisms and de Branges-Rovnyak theory
15:50–16:30 Jong Hyeon Seo (Pusan National University)
The Convergence of Relaxed Functional Iterations for Solving Quadratic Matrix
Equations with an M -matrix
1This conference was supported by Laboratory of Advanced Software in Mathematics, Institute ofMathematics for Industry, Kyushu University, JSPS KAKENHI(Grant-in-Aid for Exploratory Research)
Grant Number 25610034 and JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number25400217.

16:40–17:20 Shun’ichi Yokoyama (Kyushu University)
Computing resultant matrix of general multivariate polynomials and its determinant
using Magma
17:20–17:30 Closing（Yoshihiro Mizoguchi）
18:00 – Post-meeting party
Poster Session
Theme: Software in Mathematics Demonstration TrackSpeakers and Titles:
1. 岩下 寛弥 (九州大学大学院工学府海洋システム工学専攻) HEAP モデル法によるプル型スケジューリングプログラム
2. 山岡 幸高 (九州大学数理学府) 構文解析に特化した翻訳ソフト
3. 大塚 寛 (愛媛大学理工学研究科) TRDRD に基づくサッカーの分析ソフトウェア
4. Omar Rifki (Economic engineering department of Kyushu University) jPortRob,GetAssetsDataSet
5. 吉野 聖人 (松江工業高等専門学校 電子制御工学科) ラプラシアン固有マップ法における評価方法及びその応用
6. 田中 久治 (佐賀大学大学院工学系研究科) Coq Modules for Automata and Sticker
Systems
7. Sang-Hyup Seo (Department of Mathematics,Pusan National University) THE MONOTONE CONVERGENCE OF NEWTON’S METHOD FOR DIFFERENTIABLE
CONVEX MATRIX FUNCTIONSAbstract
Shoichi Tsuchiya (Tokyo University of Science)
Title: On Halin graphs and generalized Halin graphs
Abstract: A Halin graph, defined by Halin, is a plane graph H = T ∪ C such that Tis a spanning tree of H with no vertices of degree 2 where |T | ≥ 4 and C is a cycle
whose vertex set is the set of leaves of T . On the other hand, generalized Halingraph is a graph H = T ∪ C such that T is a spanning tree of H with no vertices ofdegree 2 where |T | ≥ 4 and C is a cycle whose vertex set is the set of leaves of T .
Note that some generalized Halin graphs may not be plane graphs, (for example,Petersen graph is a generalized Halin graph which is not planar). In this talk, weintroduce some known results on Halin graphs and generalized Halin graphs. After
that, we investigate diﬀerence between Halin graphs and generalized Halin graphs.
Shuya Chiba (Kumamoto University)
Title: On the number of components of 2-factors
in claw-free graphs Abstract: We consider only finite graphs without loops. Agraph G is said to be claw-free if G has no induced subgraph isomorphic to K1,3
(here K1,3 denotes the complete bipartite graph with partite sets of cardinalities 1and 3, respectively). A 2-factor of a graph G is a spanning subgraph of G in which
every component is a cycle.
It is a well-known conjecture that every 4-connected claw-free graph is Hamiltonian
due to Matthews and Sumner [Hamiltonian results in K1,3 -free graphs, J. Graph
Theory 8 (1984) 139–146]. Since a Hamilton cycle is a 2-factor with one component,
there are many results on the upper bounds of the number of components in 2factors of claw-free graphs. In this talk, we will present some recent results on therelationship between the number of components of a 2-factor and the minimum
degree of a graph.
Masashi Shinohara (Shiga University)
Title: On complementary Ramsey numbers Abstract: In this talk, we propose a
new generalization of Ramsey numbers which seems to be untreated in the literature.Instead of requiring the existence of a monochromatic clique, we consider theexistence of a clique which avoids one of the colors in an edge coloring.These numbers
are called complementary Ramsey numbers, and we derive their basic properties.We
also establish their connections to graph factorizations. This is a joint work withAkihiro Munemasa.
Michio Seto (Shimane University)
Title: Graph homomorphisms and de Branges-Rovnyak theory
Abstract: In 1960’s, de Branges and Rovnyak developed a theory dealing withHilbert space embedding H1 ,→ H2 . In this talk, comparing with theory of univalentfunctions, a de Branges-Rovnyak framework for study of graph homomorphisms will
be suggested. This is joint work with S. Suda and T. Taniguchi.

Jong Hyeon Seo (Pusan National University)
Title: The Convergence of Relaxed Functional Iterations for Solving Quadratic Matrix Equations with an M -matrix
Abstract: In stochastic areas, to find a special solution of a quadratic matrix equation (QME) under probabilistic constraints is one of important issues. In this paper,
first, we show the monotonic convergence of the successive approximation method(SAM[1]) to the minimal nonnegative solution of QME under nonnegativity constraints which cover two diﬀerent types of QMEs from probabilistic contexts, andexplain theoretically why the SAM is always faster than the fixed point iterative
method (FIM [2]) in numerical experimentations. Second, we present a relaxed
SAM which also preserves the monotonic convergence to the solution. Finally numerical experimentations give the new method actually improves convergence rateand is eﬀective.

参考文献[1] Bai, Z.-Z., Guo, X.-X., and Yin, J.-F. On two iteration methods for the quadraticmatrix equations. Int. J. Numer. Anal. Model. 2 (2005), 114-122.
[2] Guo, C.-H. On a quadratic matrix equation associated with an M-matrix. IMA
J. Numer. Anal. 23 (2003), 11-27.
Shun’ichi Yokoyama (Kyushu University)
Title: Computing resultant matrix of general multivariate polynomials and its determinant using Magma Abstract: We produce an eﬃcient program package tocompute the resultant matrix and its determinant for a given pair of multivariate
polynomials on Magma. This package works much more faster than the Magma’s
built-in function ”Resultant” for multivariate polynomials. We also explain some
applications of this package, and especially, try some benchmark problem for computing general formula of the discriminant. This work is in cooperation with Kinji
Kimura (Kyoto University).